The term relaxation oscillator is also applied to dynamical systems in many diverse areas of science that produce nonlinear oscillations and can be analyzed using the same mathematical model as electronic relaxation oscillators.[8][9][10][11] For example geothermal geysers,[12][13] networks of firing nerve cells,[11]thermostat controlled heating systems,[14] coupled chemical reactions,[9] the beating human heart,[11][14] earthquakes,[12] the squeaking of chalk on a blackboard,[14] the cyclic populations of predator and prey animals, and gene activation systems[9] have been modeled as relaxation oscillators. Relaxation oscillations are characterized by two alternating processes on different time scales: a long relaxation period during which the system approaches an equilibrium point, alternating with a short impulsive period in which the equilibrium point shifts.[12][11][13][15] The period of a relaxation oscillator is mainly determined by the relaxation time constant.[11] Relaxation oscillations are a type of limit cycle and are studied in nonlinear control theory.[16]

Sawtooth oscillator: In this type the energy storage capacitor is charged slowly but discharged rapidly, essentially instantly, by a short circuit through the switching device. The charging period thus takes up virtually the entire period of the waveform. The voltage across the capacitor is a sawtooth wave, while the current through the switching device is a sequence of short pulses.

Astable multivibrator: In this type the capacitor is both charged and discharged slowly through a resistor, so the output waveforms consist of two parts. The voltage generated by the capacitor is a triangle waveform, while the voltage from the switching device is a square wave.

This example can be implemented with a capacitive or resistive-capacitive integrating circuit driven respectively by a constant current or voltage source, and a threshold device with hysteresis (neon lamp, thyratron, diac, reverse-biased bipolar transistor,[25] or unijunction transistor) connected in parallel to the capacitor. The capacitor is charged by the input source causing the voltage across the capacitor to rise. The threshold device does not conduct at all until the capacitor voltage reaches its threshold (trigger) voltage. It then increases heavily its conductance in an avalanche-like manner because of the inherent positive feedback, which quickly discharges the capacitor. When the voltage across the capacitor drops to some lower threshold voltage, the device stops conducting and the capacitor begins charging again, and the cycle repeats ad infinitum.

If the threshold element is a neon lamp,[nb 1][nb 2] the circuit also provides a flash of light with each discharge of the capacitor. This lamp example is depicted below in the typical circuit used to describe the Pearson–Anson effect. The discharging duration can be extended by connecting an additional resistor in series to the threshold element. The two resistors form a voltage divider; so, the additional resistor has to have low enough resistance to reach the low threshold.

A similar relaxation oscillator can be built with a 555 timer IC (acting in astable mode) that takes the place of the neon bulb above. That is, when a chosen capacitor is charged to a design value, (e.g., 2/3 of the power supply voltage) comparators within the 555 timer flip a transistor switch that gradually discharges that capacitor through a chosen resistor (RC Time Constant) to ground. At the instant the capacitor falls to a sufficiently low value (e.g., 1/3 of the power supply voltage), the switch flips to let the capacitor charge up again. The popular 555's comparator design permits accurate operation with any supply from 5 to 15 volts or even wider.

Other, non-comparator oscillators may have unwanted timing changes if the supply voltage changes.

Alternatively, when the capacitor reaches each threshold, the charging source can be switched from the positive power supply to the negative power supply or vice versa. This case is shown in the comparator-based implementation here.

The system is in unstable equilibrium if both the inputs and outputs of the comparator are at zero volts. The moment any sort of noise, be it thermal or electromagneticnoise brings the output of the comparator above zero (the case of the comparator output going below zero is also possible, and a similar argument to what follows applies), the positive feedback in the comparator results in the output of the comparator saturating at the positive rail.

In other words, because the output of the comparator is now positive, the non-inverting input to the comparator is also positive, and continues to increase as the output increases, due to the voltage divider. After a short time, the output of the comparator is the positive voltage rail, .

Series RC Circuit

The inverting input and the output of the comparator are linked by a seriesRC circuit. Because of this, the inverting input of the comparator asymptotically approaches the comparator output voltage with a time constant RC. At the point where voltage at the inverting input is greater than the non-inverting input, the output of the comparator falls quickly due to positive feedback.

This is because the non-inverting input is less than the inverting input, and as the output continues to decrease, the difference between the inputs gets more and more negative. Again, the inverting input approaches the comparator's output voltage asymptotically, and the cycle repeats itself once the non-inverting input is greater than the inverting input, hence the system oscillates.

Rearranging the differential equation into standard form results in the following:

Notice there are two solutions to the differential equation, the driven or particular solution and the homogeneous solution. Solving for the driven solution, observe that for this particular form, the solution is a constant. In other words, where A is a constant and .

First let's assume that for ease of calculation. Ignoring the initial charge up of the capacitor, which is irrelevant for calculations of the frequency, note that charges and discharges oscillate between and . For the circuit above, Vss must be less than 0. Half of the period (T) is the same as time that switches from Vdd. This occurs when V- charges up from to .

When Vss is not the inverse of Vdd we need to worry about asymmetric charge up and discharge times. Taking this into account we end up with a formula of the form:

^When a (neon) cathode glow lamp or thyratron are used as the trigger devices a second resistor with a value of a few tens to hundreds ohms is often placed in series with the gas trigger device to limit the current from the discharging capacitor and prevent the electrodes of the lamp rapidly sputtering away or the cathode coating of the thyratron being damaged by the repeated pulses of heavy current.

^Trigger devices with a third control connection, such as the thyratron or unijunction transistor allow the timing of the discharge of the capacitor to be synchronized with a control pulse. Thus the sawtooth output can be synchronized to signals produced by other circuit elements as it is often used as a scan waveform for a display, such as a cathode ray tube.

And that's the essence of the “relaxation oscillator” — it's a simple feedback oscillator that takes advantage of the inverter's hysteresis and is slowed down by charging up a capacitor. And here's what it sounds like. I used a potentiometer for the ...

Up to now, we've been changing the resistance in the feedback loop of our relaxation oscillator circuit to control the pitch. But what if we don't want to have to control the pitch by hand anymore? We can pass off resistor-selection duties to a switch ...

At the core of the circuit, MOSFET driver U1 with a Schmitt trigger input is used to drive the MOSFET, and forms a relaxation oscillator with Q2, R8, R9, and C3. With the component values shown, the duty cycle is approximately 5% at a cycle time of 20ms.

And can recognise in the irregular sawtooth of ice age temperature record a system that looks remarkably like a nasty multiple (negative) feed back time delayed relaxation oscillator. Oscillators don't need external inputs to change, they do that ...

The magnetar 1E 2259+586 shines a brilliant blue-white in this false-color X-ray image of the CTB 109 supernova remnant, which lies about 10,000 light-years away toward the constellation Cassiopeia. CTB 109 is only one of three supernova …more.

The motor, a surface-tension-driven nanoelectromechanical relaxation oscillator, was built by a team of researchers led by Alex Zettl at the University of California, Berkeley. Although the amount of energy produced is small -- 20 microwatts -- it is ...

The TL431 is a three-terminal programmable shunt regulator that implements Zener-like references with low temperature coefficients. Its output can be programmed from the internally set reference of about 2.5V to 36V using two external resistors. In ...

Limit to books that you can completely read online
Include partial books (book previews)